Homology of Distributive Lattices

Jozef H. Przytycki; Krzysztof K. Putyra

doi:10.1007/s40062-012-0012-5

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arXiv · 1111.4772

Homology of Distributive Lattices

Jozef H. Przytycki·Krzysztof K. Putyra

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Abstract

We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology of a finite distributive lattice. We also indicate the answer for unital spindles and conjecture the general formula for semi-lattices and some skew lattices. Then we propose a generalization of a lattice as a set with a number of idempotent operations satisfying the absorption law.

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BibTeX RIS

Jozef H. Przytycki, Krzysztof K. Putyra. 2011-11-21. Homology of Distributive Lattices. https://doi.org/10.1007/s40062-012-0012-5

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